Simplify the following expression: $\dfrac{42t^4}{21t^3}$ You can assume $t \neq 0$.
Explanation: $ \dfrac{42t^4}{21t^3} = \dfrac{42}{21} \cdot \dfrac{t^4}{t^3} $ To simplify $\frac{42}{21}$ , find the greatest common factor (GCD) of $42$ and $21$ $42 = 2 \cdot 3 \cdot 7$ $21 = 3 \cdot 7$ $ \mbox{GCD}(42, 21) = 3 \cdot 7 = 21 $ $ \dfrac{42}{21} \cdot \dfrac{t^4}{t^3} = \dfrac{21 \cdot 2}{21 \cdot 1} \cdot \dfrac{t^4}{t^3} $ $\phantom{ \dfrac{42}{21} \cdot \dfrac{4}{3}} = 2 \cdot \dfrac{t^4}{t^3} $ $ \dfrac{t^4}{t^3} = \dfrac{t \cdot t \cdot t \cdot t}{t \cdot t \cdot t} = t $ $ 2 \cdot t = 2t $